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The circumference of a circle whose area is 81 $π r 2$ is:

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9πr

18πr

3πr

81πr

answer is B.

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Detailed Solution

Given, a circle whose area is 81

π r 2

.
We know that the area of a circle with ‘r’ radius is

π

times the square of its radius i.e.,

π r 2

.
Now, as per the question, let us assume the radius of the circle as ‘R’.
So, using the formula for the area and given area i.e.,

π R 2 = 81 π r 2 R 2 = 81 π r 2 π R 2 = 81 r 2 R = 81 r 2 R = 9 r ........... (i)

Now, the circumference of the circle with radius ‘R’ will be

2 π R

i.e.,

= 2 π 9 r = 18 π r

Therefore, the circumference of the circle with area 81

π r 2

is obtained as

18 π r

.
Hence, the correct option is (2).

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